{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Flux discretizations"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We showcase the different alternatives for the discretization of fluxes in PorePy. To this aim, we focus on single-phase flow in unfractured domains. <br>\n",
    "We consider three discretization schemes:\n",
    "* two-point flux approximation\n",
    "* multi-point flux approximation\n",
    "* dual virtual element method\n",
    "\n",
    "Mixed finite elements of the lowest order, a.k.a RT0-P0, are supported in PorePy, but not demonstrated herein. While this tutorial considers a 2d domain, most of the code works for 1d, 2d, and 3d domains. The case of mixed-dimensional domains containing both fractures and a porous medium is covered in the [single phase flow](./single_phase_flow.ipynb) tutorial. \n",
    "\n",
    "## Problem statement\n",
    "\n",
    "Let $\\Omega$ be a regular domain with boundary $\\partial \\Omega$. The boundary can be divided in two non-overlapping parts on which we will impose Dirichlet ($\\partial \\Omega_d$) and Neumann ($\\partial \\Omega_n$) boundary conditions, respectively. We indicate with $\\mathbf{n}$ the outward unit normal vector of $\\partial \\Omega$.<br>\n",
    "The single-phase flow can be written in\n",
    "* using two primary variables:\n",
    "$$\\nabla \\cdot \\mathbf{u} = f \\qquad \\mathbf{u} = - K \\nabla p$$\n",
    "with boundary conditions on $\\partial \\Omega_d$ and $\\partial \\Omega_n$:\n",
    "$$ p = p_b \\qquad \\mathbf{u} \\cdot \\mathbf{n} = u_b$$\n",
    "* or with a single primary variable:\n",
    "$$ - \\nabla \\cdot K \\nabla p = f $$\n",
    "with boundary conditions on $\\partial \\Omega_d$ and $\\partial \\Omega_n$:\n",
    "$$ p = p_b \\qquad - K \\nabla p \\cdot \\mathbf{n} = u_b$$\n",
    "\n",
    "Here, $f$ is a scalar source/sink term, $K$ is the permeability matrix, $p_b$ is the pressure at the boundary (Dirichlet condition), and $u_b$ is the flux at the boundary (Neumann condition).<br>\n",
    "\n",
    "We present *step-by-step* how to create the grid, declare the problem data, and finally solve the problem. <br><br>\n",
    "\n",
    "For the example we assume: $\\Omega$ as presented below, $\\partial \\Omega_d = \\partial \\Omega$, $\\partial \\Omega_n = \\emptyset$, with data: $f = 1$, $K = I$ and $p_b = 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import basic modules"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before creating the grid we import NumPy, the SciPy sparse library and PorePy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.sparse as sps\n",
    "import porepy as pp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creation of the grid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We specify the number of cells in each dimension and the physical size of the domain. Then we create a Cartesian grid and compute geometric properties such as face centers, cell volumes etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "Nx = Ny = 20\n",
    "phys_dims = [1, 1]\n",
    "g = pp.CartGrid([Nx, Ny], phys_dims)\n",
    "g.compute_geometry()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We plot the grid using the interface with matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp.plot_grid(g, plot_2d=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Define the problem data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We declare the permeability matrix $K$, the scalar source term $f$, and the boundary conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Permeability\n",
    "perm = pp.SecondOrderTensor(np.ones(g.num_cells))\n",
    "\n",
    "# Unitary scalar source already integrated in each cell\n",
    "f = g.cell_volumes\n",
    "\n",
    "# Boundary conditions\n",
    "b_faces = g.tags[\"domain_boundary_faces\"].nonzero()[0]\n",
    "bc = pp.BoundaryCondition(g, b_faces, [\"dir\"] * b_faces.size)\n",
    "bc_val = np.zeros(g.num_faces)\n",
    "\n",
    "# Collect all parameters in a dictionary\n",
    "parameters = {\n",
    "    \"second_order_tensor\": perm, \n",
    "    \"source\": f, \n",
    "    \"bc\": bc, \n",
    "    \"bc_values\": bc_val\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once all the data are created we group them in a dictionary, where the keyword `\"flow\"` represent the physical process considered and ensures that the discretization objects use the correct parameters. Note that the call to `initialize_default_data` assigns default values to the flow parameters which are not specified. This means that we could have omitted the specification of `\"bc_values\"` and `\"second_order_tensor\"`, since we have assigned the default values for these."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_key = \"flow\"\n",
    "data = pp.initialize_default_data(g, {}, data_key, parameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section we present all the approaches to solve the problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two-point flux approximation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two-point flux approximation solves the single-phase flow problem using pressure as the primary variable. We use this to discretize the flux term, before assembling it. The source term is passed directly without any need for discretization. The ensuing system of linear equations is solved for pressures using a direct sparse solver."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "flow_discretization = pp.Tpfa(data_key)\n",
    "flow_discretization.discretize(g, data)\n",
    "A, b_flow = flow_discretization.assemble_matrix_rhs(g, data)\n",
    "\n",
    "b_rhs = data[pp.PARAMETERS][\"flow\"][\"source\"]\n",
    "\n",
    "p_tpfa = sps.linalg.spsolve(A, b_flow + b_rhs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We visualize the solution using the plot grid function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp.plot_grid(g, p_tpfa, plot_2d=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consistency check (included to detect if this tutorial is broken):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert np.isclose(np.sum(p_tpfa), 14.192684340967551)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multi-point flux approximation "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The multi-point flux approximation also uses pressure as the only primary variable. We discretize the flux term anew with the MPFA, and assemble the matrix. Note that the call to Mpfa.discretize() will override the already stored discretization matrix for Tpfa. We reuse the source term discretization, as this is the same for TPFA and MPFA."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "flow_discretization = pp.Mpfa(data_key)\n",
    "flow_discretization.discretize(g, data)\n",
    "A, b_flow = flow_discretization.assemble_matrix_rhs(g, data)\n",
    "\n",
    "p_mpfa = sps.linalg.spsolve(A, b_flow + b_rhs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To represent the solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp.plot_grid(g, p_mpfa, plot_2d=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consistency check:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert np.isclose(np.sum(p_mpfa), 14.192684340967542)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dual virtual element method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dual virtual element method solves the single-phase flow problem using both pressures and fluxes as primary variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "flow_discretization = pp.MVEM(\"flow\")\n",
    "flow_discretization.discretize(g, data)\n",
    "A, b_flow = flow_discretization.assemble_matrix_rhs(g, data)\n",
    "\n",
    "rhs_discretization = pp.DualScalarSource(\"flow\")\n",
    "\n",
    "data[pp.PARAMETERS][\"flow\"][\"source\"] = data[pp.PARAMETERS][\"flow\"][\"source\"]\n",
    "rhs_discretization.discretize(g, data)\n",
    "_, b_rhs = rhs_discretization.assemble_matrix_rhs(g, data)\n",
    "\n",
    "up = sps.linalg.spsolve(A, b_flow + b_rhs)\n",
    "\n",
    "# Extract the normal flux and pressure from the solution\n",
    "u_mvem = flow_discretization.extract_flux(g, up, data)\n",
    "p_mvem = flow_discretization.extract_pressure(g, up, data)\n",
    "\n",
    "# For visualisation purpose project the flux on a vector piecewise constant field\n",
    "P0u = flow_discretization.project_flux(g, u_mvem, data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To represent the pressure and velocity solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/michealoguntola/porepy/src/porepy/viz/plot_grid.py:193: UserWarning: Attempting to set identical low and high zlims makes transformation singular; automatically expanding.\n",
      "  ax.set_zlim3d(z)  # type: ignore[attr-defined]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp.plot_grid(g, p_mvem, P0u * 0.2, figsize=(15, 12))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consistency check:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert np.isclose(np.sum(p_mvem), 14.348068220560325)\n",
    "assert np.isclose(np.sum(u_mvem), 0)\n",
    "assert np.isclose(np.sum(P0u), 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What we have explored\n",
    "Elliptic equations (e.g., diffusion) in PorePy are specified in terms of a mesh, a second order diffusion tensor, source terms and boundary conditions, all of which must be assigned with a specific syntax. To discretize the equations, PorePy provides two- and multi-point finite volume discretizations as well as the lowest order mixed virtual element method. Discrete solutions are obtained by first discretizing, then assembling and solving the equations."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
